Reading 7: Statistical Concepts and Market Returns-LOS i 习题 2011, face, interpret, variation, center

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Session 2: Quantitative Methods: Basic Concepts
Reading 7: Statistical Concepts and Market Returns

LOS i: Define, calculate, and interpret the coefficient of variation and the Sharpe ratio.

 

 

Given a population of 200, 100, and 300, the coefficient of variation is closest to:

A) 30%.

B) 100%.

C) 40%.

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CV = (σ/mean)
mean = (200 + 100 + 300)/3 = 200
σ = √[(200 - 200)² + (100 - 200)² + (300 - 200)² / 3] = √6666.67 = 81.65
(81.65/200) = 40.82%

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The mean monthly return on (U.S. Treasury bills) T-bills is 0.42% with a standard deviation of 0.25%. What is the coefficient of variation?

A) 84%.

B) 60%.

C) 168%.

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The coefficient of variation expresses how much dispersion exists relative to the mean of a distribution and is found by CV = s / mean, or 0.25 / 0.42 = 0.595, or 60%.

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An investor is considering two investments. Stock A has a mean annual return of 16% and a standard deviation of 14%. Stock B has a mean annual return of 20% and a standard deviation of 30%. Calculate the coefficient of variation (CV) of each stock and determine if Stock A has less dispersion or more dispersion relative to B. Stock A's CV is:

A) 0.875, and thus has less dispersion relative to the mean than Stock B.

B) 1.14, and thus has more dispersion relative to the mean than Stock B.

C) 1.14, and thus has less dispersion relative to the mean than Stock B.

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CV stock A = 0.14 / 0.16 = 0.875

CV stock B = 0.30 / 0.20 = 1.5

Stock A has less dispersion relative to the mean than Stock B.

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The mean monthly return on a sample of small stocks is 4.56% with a standard deviation of 3.56%. What is the coefficient of variation?

A) 128%.

B) 84%.

C) 78%.

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The coefficient of variation expresses how much dispersion exists relative to the mean of a distribution and is found by CV = s / mean. 3.56 / 4.56 = 0.781, or 78%.

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If stock X's expected return is 30% and its expected standard deviation is 5%, Stock X's expected coefficient of variation is:

A) 6.0.

B) 0.167.

C) 1.20.

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The coefficient of variation is the standard deviation divided by the mean: 5 / 30 = 0.167.

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What is the coefficient of variation for a distribution with a mean of 10 and a variance of 4?

A) 40%.

B) 25%.

C) 20%.

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Coefficient of variation, CV = standard deviation / mean. The standard deviation is the square root of the variance, or 4^? = 2. So, CV = 2 / 10 = 20%.

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If the historical mean return on an investment is 2.0% and the standard deviation is 8.8%, what is the coefficient of variation (CV)?

A) 1.76.

B) 6.80.

C) 4.40.

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The CV = the standard deviation of returns / mean return or 8.8% / 2.0% = 4.4.

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A portfolio of options had a return of 22% with a standard deviation of 20%. If the risk-free rate is 7.5%, what is the Sharpe ratio for the portfolio?

A) 0.568.

B) 0.725.

C) 0.147.

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Sharpe ratio = (22% – 7.50%) / 20% = 0.725.

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A higher Sharpe ratio indicates:

A) lower volatility of returns.

B) a higher excess return per unit of risk.

C) a lower risk per unit of return.

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The Sharpe ratio is excess return (return ? R_f) per unit of risk (defined as the standard deviation of returns).

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A portfolio has a return of 14.2% and a Sharpe’s measure of 3.52. If the risk-free rate is 4.7%, what is the standard deviation of returns?

A) 2.7%.

B) 3.9%.

C) 2.6%.

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Standard Deviation of Returns = (14.2% – 4.7%) / 3.52 = 2.6988.